Solving Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines coincide, or are the same line.

Front

How do you graph a linear equation in slope-intercept form?

Back

Identify the slope (m) and y-intercept (b) from the equation y = mx + b.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.

Front

What is the y-intercept of the line represented by the equation y = -x + 5?

Back

The y-intercept is 5.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve.